Structured least squares to improve the performance of ESPRIT-type high-resolution techniques

ESPRIT type high-resolution (spatial) frequency estimation techniques, like standard ESPRIT, state space methods, matrix pencil methods, or Unitary ESPRIT, obtain their (spatial) frequency estimates from the solution of a highly-structured, overdetermined system of equations. Here, the structure is defined in terms of two selection matrices applied to a matrix spanning the estimated signal subspace. Structured least squares (SLS) is a new algorithm to solve this overdetermined system, the so called invariance equation, by preserving its structure. Simulations confirm that SLS outperforms the least squares (LS) and total least squares (TLS) solutions of this invariance equation, since the accuracy of the resulting (spatial) frequency estimates and the accuracy of the underlying signal subspace are improved significantly. Furthermore, SLS can be used to improve the accuracy of adaptive frequency estimating schemes that are based on fast adaptive subspace tracking techniques. Moreover, SLS has been extended to the two-dimensional (2-D) case to be used in conjunction with 2-D Unitary ESPRIT, an efficient ESPRIT-type algorithm that provides automatically paired 2-D (spatial) frequency estimates